Copernicus On The Science Of STAR TREK INTO DARKNESS!!

For those who don’t know me, I occasionally write movie reviews for Ain’t It Cool News, but I’m also a professional astronomer. I occasionally write articles on the science of movies (most recently, AVENGERS), not because I want to nitpick at every little thing, but because it is a good chance to sneak in a little knowledge about how the universe works. But I also do it because I get annoyed when writers get lazy and don’t think twice or talk to a scientist, and as a result produce movies that are way less cool than they ought to be. And at the same time, I want to celebrate those awe-inspiring moments in movies that do mean more if they are based in real science.

NIBIRU, SERIOUSLY?

Sadly, right from the title card you can tell STAR TREK INTO DARKNESS has disdain rather than respect for science. The planet Kirk and company are there to interfere with is named Nibiru. This is a made up idea by some certified nutbars who have claimed that it is a rogue planet variously hiding in our own solar system(!) or about to zoom through it, somehow ending life on Earth by bringing about a “pole shift,” or some such bullshit. Nibiru was originally mixed up in this Comet Hale-Bopp craziness in 1997, then it was claimed it would destroy humanity in 2003, and then people attached it to 2012 Maya stupidity.

I know Bob Orci, one of the writers of Star Trek, is a conspiracy nut. We’ve gotten into arguments about whether the Big Bang happened. Maybe he was just trolling professional astronomers by slipping Nibiru in there? After all, he didn’t like my take on the science of the 2009 STAR TREK, even though I was positive on the movie. I don’t care what the reason is -- stunts like this are a slap in the face to what made Star Trek great in the first place. One of the many legacies of Star Trek is thousands of astronomers and astronauts who were inspired to devote their lives to uncovering the awe and wonder of the universe because of the show’s message of cooperation and exploration. Shame on you, JJ Abrams and Bob Orci, for defiling the legacy of Star Trek by valuing lazy delusional paranoia over its true principles: critical thinking and reason.

THE VULCAN-OLOGIST

According to the dialogue near the beginning of the film, a volcano is about to erupt on the planet that will wipe out all life on it, or at least civilization. Is this plausible? It is true that large volcanic eruptions over Earth’s history have killed tens of thousands of locals at a time. And Earth’s history is filled with records of volcanic eruptions affecting temperatures globally, sometimes for years after the eruption. Effects have even included the “year without a summer.” Some have speculated that the one of the largest known volcanic eruptions in Earth’s history, the Toba event from about 70,000 years ago, was responsible for a genetic bottleneck in human mitochondrial DNA. However, that idea seems to be contradicted by other evidence, so isn’t widely believed.

But what about other planets? At 14 miles high and covering the size of France, Olympus Mons on Mars makes Earth volcanoes look puny in comparison. And Venus may have been resurfaced by volcanism about 500 million years ago. Io, a moon of Jupiter, is constantly being repaved by sulphur-spewing volcanoes. Some shoot so high, they almost launch material into orbit.

But all of these scenarios have problems for wiping out all life on a planet. It takes many volcanic eruptions to cause catastrophic global effects. So stopping just one won’t do very much in the long term. On a volcanically active planet, there will be more.

Well, what if the planet were much smaller than Earth? Could you wipe out all life then? There are two problems with that -- one is that the surface gravity would be lower, so we’d see Kirk and crew bouncing all around. And the second is that small planets cool faster (that depends on the ratio of surface area to volume) and so don’t have a molten core, or volcanism, for long -- not on human evolutionary timescales. What about Io, you say? As a moon of Jupiter, it isn’t huge. That’s true, but its interior doesn’t cool because it is constantly heated by tidal forces from Jupiter.

What if all the humanoids only occupy a small region of the planet? That’s problematic because they would have been prone to catastrophe in the past. Basically, if life evolves on a planet for billions of years, it has to be stable on billion year timescales against catastrophes wiping out all life, even if it might have the occasional devastating event.

But the real problem is that if a planet is that volcanically active, plugging up a single volcano (a) isn’t likely to work, and (b) is just a short term solution. Why isn’t it likely to work? Let’s calculate how much energy is in a supervolcanic eruption -- the kind that didn’t even succeed at wiping out humans, but was the best the Earth could do. These explosions measure an 8 (the highest ranking) on the Volcanic Explosivity Index, and are thought to eject 1000 cubic kilometers of stuff more than 25 km high.

Great, we can estimate how much energy this is! It is just gravitational potential energy: U=mgh, where m=mass, h=height, and g=acceleration due to gravity (9.8 m/s2). How much does 1000 cubic kilometers of the Earth’s mantle weigh? The density is about 4000 kg per meter cubed. And there are a billion cubic meters in a cubic kilometer. So we have m = 4000 km/m3 (1000 km3) (109 m3 / km3) = 4x1015 kg. In round numbers, that makes the energy, U = mgh = 4x1015 kg (10 m/s2) (25,000 m) = 1021 J. A large nuclear weapon releases about 1017 J. So this volcano has the energy of about 10,000 of the largest nuclear weapons. That’s about how many there are on Earth. So basically, Spock’s little ice plug has to hold back the equivalent energy of all the nuclear weapons on Earth. And the newly-frozen surface that he’s standing beside is just the tip of the iceberg. And heat is just a small part of it. There are massive pressure forces in the planet too.

So he isn’t likely to succeed. But if he could, how would he go about it? There are endothermic reactions on Earth, like those “ice packs” that aren’t ice at all, but chemicals in a container you can break to mix them and turn the thing cold. That absorbs heat to change chemical bonds, but it is too inefficient for the amount of energy absorption we need here. And besides, they tell us that this is a “cold fusion device.” Ok, that makes no sense. Cold fusion, has of course been debunked -- this sounds like just another Orci / Abrams attempt at getting crackpottery being discussed by more people (see FRINGE). And besides, cold fusion is supposed to gain energy, not absorb it.

But ok, if I had to design something that you might call a “cold fusion device,” and have it get rid of energy, how would it work? Well, iron-56 is the most tightly bound atomic nucleus. Every time you fuse two nuclei lighter than that together, you get energy. That’s what powers the sun. Only hydrogen and helium (and a little lithium) were created in the Big Bang. All the other elements up to iron were forged in a star. But stellar fusion only works up to iron. If you try to fuse any two elements to make something heavier than that, you lose energy instead of gaining it. But you can do fusion beyond iron inside a certain kind of supernova (which is what I study professionally). That’s how we get all the elements heavier than iron. Take gold, for example. It was created in a supernova -- but it took energy to produce it.

So my idea for a “cold fusion device” would be to do just that: the kind of fusion where you absorb energy instead of gaining it. Looking at this chart, to get the biggest energy sink, we want to somehow fuse iron-56 (binding energy 8.8 Megaelectron Volts (MeV) per nuclear particle, or nucleon) to uranium-238 (7.6 MeV per nucleon). Doing that, we can absorb 8.8-7.6 = 1.2 MeV / nucleon = 2 x 10-13 Joules (J) / nucleon. To absorb 1021 J, it would take 1021 J / 2 x 10-13 J per nucleon = 5 x 1033 nucleons. Since Fe-56 has 56 nucleons (protons and neutrons) per atom, it would take 5 x 1033 / 56 = 1032 atoms of iron. A mole of iron (6 x 1023 atoms) has 56 g of it, so 56g (1032 atoms) / (6 x 1023 atoms) = 1010 g = 107 kg = 2 x 107 lb. So to absorb all the energy in the volcano, Spock’s “cold fusion device” would have to weigh 20 million pounds! He’d start with that much iron and end up with about that much uranium. If he wanted to be an alchemist, he could start with a bigger bomb and turn it all into gold. (Medieval alchemists failed because they didn’t have hot enough ovens).

Also: why didn’t they just beam the “bomb” right into the volcano? They couldn’t beam into the volcano because they needed a direct line of sight? Bullshit, the Enterprise beams people through entire planets on a daily basis. You never hear: “Beam me up, Scotty.” “But Cap’n we have to wait until our orbit is above your position, so hold on for an hour or so.” And if so, big deal, fly over the damn thing and beam it in. And don’t give me some BS about how Spock had to arm it. We already have volcano-exploring robots. No, correction, we already had them twenty friggin years ago.

WE ALL LIVE IN A YELLOW ENTERPRISE

But now here’s the really ridiculous part. Why was the Enterprise hiding underwater? It makes no goddamn sense. You can’t transmit electromagnetic waves underwater, at least not normal ones, since saltwater attenuates them. This is a huge problem for submarines. Normal radio communications don’t work. Only extremely low frequency (ELF) waves (3-300 Hz) will penetrate a significant distance undersea. Because of the low frequency, these transmissions have low bit rates -- you can only transmit text, and only a few characters a minute. And it is one-way -- from a land base to a submarine -- the tricks you have to use to do this are such that you couldn’t have a transmitter on a sub. So the messages tend to be short -- like “surface” or “send a buoy to the surface to communicate.” Or, my favorite, go to the underwater telephone! They have these stations set up where they can communicate acoustically. You can’t reply using ELF from the sub because these are very long wavelength waves -- thousands of kilometers. You’d need an antenna a good fraction of the size of the Earth to transmit. The US military had a batshit insane plan, Project Sanguine, to build 6000 miles of antenna covering 40% of the state of Wisconsin, powered by 10 underground power plants. They ended up devising another trick, using the Earth itself to act as part of the antenna. Now they probably use HAARP to make the ionosphere into an antenna.

In the actual movie, I think they can still communicate with the Enterprise underwater (fine, who knows how those damn communicators work -- they do have “subspace” communications in Star Trek after all), but they can’t use the transporters. Indeed you couldn’t -- those things have to be either beamed energy or matter, and that wouldn’t work underwater.

But you know else wouldn’t work underwater? Everything! Take thrusters, for example, which are simple plasma jets that we see working later in the movie. Or the shields, which are no doubt electromagnetic (as opposed to the metal and kevlar shields on the International Space Station). I’m just giving them the fact that the force fields that provide structural integrity when the ship experiences extreme accelerations can save them from the underwater pressure.

But the main point is that, as every engineer knows, if you are building something, every new requirement forces you to make design tradeoffs. So if you are building mankind’s foremost tool for exploring vast distances in the galaxy, you want it to excel at that. You can’t have the design compromised by all these idiotic things that would allow it to go underwater just in case there was a sub-moron for a starship captain. This is why you never see flying cars, car-boats, airplane-boats, ship-trains, etc., outside of a few nuts who don’t understand this design principle. It is *way* better to design a boat that is good at being a boat and a car that is good at being a car, instead of something that sucks at both.

And the only reason they were underwater was to hide!?! You don’t have to hide when you can friggin’ orbit and you are dealing with a paleolithic society. And how, exactly, are you hiding, when you are parked right next to this giant settlement of people! You had to get down there and get out somehow? And by hiding in the water, you give up your most important ability. The ability to fucking teleport! Oh you’ve got some arrows? That’s nice, I can DISAPPEAR! Jesus this version of Kirk is criminally stupid. Oh and one other thing. This isn’t science, but I can’t help myself. The real Kirk wouldn’t run from tribesmen, or any other threat for that matter.

Interestingly enough, when Kirk and Bones jump in the water, they rocket down to the Enterprise. Jet boots! I was watching the movie with my friend and fellow astrophysicist, Ben Mazin, who invented something called Jet Boots -- a diving propulsion system used by militaries. He flipped out. Real-world Jetboots don’t emit bubbles, but the ones on Star Trek do. This raises the question -- why were Kirk and Bones wearing this underwater propulsion system in the first place? Seems like they knew they were going to have to jump off a cliff and swim to the enterprise. So that monster they were going to hitch a ride on was only to take them a few hundred meters? Sounds like a ridiculous plan.

Also, would they be ok from the pressure if they zoomed down underwater like that? Remarkably, yes! People have free-dived hundreds of meters. Your lungs shrivel into a tiny ball from the pressure, but blood plasma seeps in, keeping them from completely collapsing and damaging them. Free divers can go much farther down than SCUBA divers, because they aren’t breathing the high pressure air that divers breathe. That leads to nitrogen dissolved in the bloodstream, and when you try to rise too quickly, you could get the bends. Now, once Kirk and McCoy were onboard the submerged Enterprise, they, along with the rest of the crew, would be breathing high pressure air. So there’s a limit to how fast the Enterprise could safely rise, which would decrease the pressure. And even then, nitrogen would remain in the bloodstream of all the crew members on the Enterprise for 24 hours. You aren’t supposed to fly for 24h after diving (much less go into space), because the low cabin pressure on airplanes would cause that nitrogen to outgass from your blood and tissues and give you the bends. So, good job, Kirk, you’ve killed the entire crew because of your stupid desire to take the Enterprise underwater.

THESE PEOPLE DON’T UNDERSTAND THE CONCEPT OF WARP

Ok, we know from relativity that you can’t travel faster than light. The way around that in the Star Trek universe is that you warp space, kind of folding it and shortening the distance between two points. Then you are actually going at sublight speeds in the warp bubble, but the in another reference frame you are going faster than the speed of light. That’s why Trek ships are designed the way they are -- these enormous space-warping nacelles are kept separate from engineering and the crew quarters.

This has a few consequences. For one, you can’t just warp right out of spacedock. This is quite well established in all previous incarnations of STAR TREK. Can you imagine what warping space around a spacedock would do? Oh let’s take all the space this dock is contained in and collapse it all together! WRATH OF KHAN showed how you pilot a ship out of spacedock.

What a masterful scene that is. In just a few minutes it simultaneously: shows off the majesty of the Enterprise, establishes how Kirk is truly no longer in command of the Enterprise and is uncomfortable with it, “humanizes” Lt. Saavik as being completely unexperienced despite her overconfident demeanor, shows that this scenario where Spock is in command, but Kirk is on the Enterprise, is awkward, provides no small measure of verisimilitude by drawing parallels between a space ship and a seafaring vessel, and on top of it all, allows the score to soar! This is the problem with STAR TREK INTO STUPIDITY in a nutshell. It discards these key moments that ground the characters in humanity, ground the fantastic elements in both the lore of the series and parallels to our reality, and provide breathing room and awe.

In fact, they don’t even like to go to warp inside the solar system in real STAR TREK. The stated reason is that they could run into something, like an asteroid. But it makes sense for another reason too. These ships are analogous to boats. In a real boat, you don’t just go cruising at top speed through an area with a lot of other boats, or a residential area, because you make waves that are really annoying and possibly damaging to anyone who lives there. There is an is an analogous situation with gravitational waves. Einstein’s theory of relativity says that gravity distorts spacetime. Once prediction is that orbiting neutron stars or black holes produce gravitational waves -- ripples in the very fabric of spacetime. But it isn’t just orbiting superdense bodies, any large spacetime disturbance ought to do it, like, say, warping it to send a starship to superluminal speeds. Hulse and Taylor won the Nobel Prize in 1993 for showing that two orbiting neutron stars are losing energy and spiraling into each other due to the radiation of gravitational waves. We haven’t detected gravitational waves directly yet, but this may happen with the Advanced LIGO detectors come online in 2014.

DROP OUTS

It isn’t super-well established where Kronos is in Star Trek lore. The most direct statement is that in STAR TREK: ENTERPRISE, Archer says it is 4 days away at warp 4.5. Since that is about 80 times the speed of light, that puts it at 80*300,000 km/s * 345,600 s in 4 days / 9.4e12 km/ly = 0.88 lighyears (ly). That makes no sense -- the closest star to the Sun is about 4 lightyears away. Kronos must be less than 90 ly away, because at some point on Enterprise, after they’ve visited Kronos, they say 90 ly is the farthest they’ve traveled. Let’s be relatively conservative and say Kronos is only 10 ly away.

They get back from Kronos to Earth in about a minute in STAR TREK INTO DARKNESS. How fast are they traveling? If it would normally take you 10 years to get there, traveling at the speed of light, instead they do it faster by the number of seconds in 10 years divided by 60s in a minute. that’s c*3e8s/60s = 5 million times the speed of light. And remember that is pretty much a lower limit because I chose such a close distance for Kronos. That’s thousands of times faster than Starfleet ships are supposed to go, even the ones in the far future. Our galaxy is about 100,000 lyr across. At that speed you could cross it in 7 days. So much for the plot of the entire run of STAR TREK: VOYAGER!

And another ridiculously stupid thing about the plot: they drop out of warp (actually they are kind of shot out, they don’t seem to actually try to stop the Enterprise), almost on top of the Moon. The radius of the moon is 1700 km and it fills up the screen, so they must have been about 1000 km away from it. Traveling at the speed above, if they had come out of warp literally one nanosecond later, they would have crashed into the moon. Even if we want to be really ridiculous and say they were only traveling at the speed of light, they would have crashed into the moon 0.003 seconds later.

And then! To top it off, they start crashing into, what? Not the Moon, the Earth! I *think* some character mumbles something about them being caught in the Earth’s gravity, and they are all the sudden being pulled in. Here’s where the movie gets a little cloudy, or maybe it is just my understanding of what was supposed to be going on. Within a few minutes they are pulled from right next to the Moon all the way into the Earth’s atmosphere. This is just insane

Rather than go through some equations about how long this would take, instead we can just look at the case of Apollo 13. We launched a rocket from Earth, and due to a catastrophic failure of one of the oxygen tanks, they had to abort their lunar landing mission and move to a “free return” trajectory around the moon, and back to Earth. “Free return” just means that you don’t have to fire the rockets to return to Earth, you just use lunar gravity to swing you back around to Earth, with some minor course corrections. This is cool, because it tells us how long it takes a spaceship to “fall” back to Earth from the moon, if it can’t use its engines! In the case of Apollo 13, it took about 64 hours. Actually, that’s faster than it otherwise would have, because they did burn the descent engine two hours after swinging around the moon to speed their return to Earth by 10 hours. Anyway, the bottom line is that it takes *days*, not minutes, for a spacecraft to fall to Earth from lunar orbit.

ANGULAR MOMENTUM

When the Enterprise is falling into the Earth, it looks like it is falling straight into it, as if the two are balls on a string being drawn to each other. That’s not the way two bodies gravitationally attracted to each other work -- they approach each other on curved paths. Have you ever wondered why everything in space orbits something? It is because of conservation of angular momentum.

The most famous terrestrial example is an ice skater spinning. When she draws in her outstretched arms, she starts spinning faster and faster. The same thing would happen to the Enterprise as it fell to Earth. It wouldn’t fall straight in, it would kind of orbit. If it didn’t have the energy to make a complete orbit, it would still sort of half-loop around the Earth, and come in at an angle.

What energy would it have? Ignoring vectors, the formula for angular momentum (L) is L=rmv, where r is the distance from the axis of rotation to the thing rotating around it, m is the mass, and v is the velocity perpendicular to the line defined by r. We can make a ratio of the angular momentum at the Moon’s orbit and the angular momentum as the Enterprise enters the Earth’s atmosphere. Then, since angular momentum is conserved, and mass is conserved, these two quantities cancel. We’re left with vE=vM*(rM/rE). The ratio of the distance to the Moon to the Earth’s radius is about 60. That means whatever transverse velocity the Enterprise had at the orbit of the Moon would be amplified by a factor of 60 by the time it reached Earth, just due to conservation of angular momentum.

Would they have even crashed into the Earth? The escape velocity of the Earth (the velocity needed to achieve orbit) is about 7 km/s if you are already in space (it is higher if you have to leave the surface). And 7 km/s / 60 = about 100 m/s. So if the Enterprise was traveling at 100 meters per second or more relative to the Earth when it was at the Moon’s orbit, it never would have fallen all the way to the Earth, it would have attained orbital velocity by the time it reached the atmosphere. One hundred meters per second is not very fast -- that’s only ten times faster than a human can run! That’s nothing for a ship that just dropped out of warp and is being hit by projectiles. Just shoot a photon torpedo in the opposite direction and let the back reaction give you the tiny push to remain in orbit.

Fine, so you have to have them actually crash into Earth, because the script calls for it. My point is, show them streaking into the atmosphere at an angle, not falling directly down on the Earth. It is a small thing, but to anyone who knows science, it is glaring, and just shows that most people who worked on this movie know very little about physics and didn’t talk to anyone who did.

BEAM ME ACROSS THE GALAXY, SCOTTY

In the original STAR TREK series, they didn’t have the budget to show the Enterprise landing in every episode, so they invented transporters that could beam characters to the surface. But to keep this from becoming a solution to any problem, it had to have limitations: you can only do it over short distances, in certain conditions, etc. There was a bit of silliness involved, because it meant that every episode they had to lose communication with the ship or lose transporter functionality.

In STAR TREK (2009), the writers wrote themselves out of a plot hole by disregarding the way beaming works, deciding that their Scotty was so smart he came up with a way to beam people anywhere, any time. This is a classic example of sacrificing the future to pay for the present. To the (sort of) credit of the creators of STAR TREK OUT OF SANITY, they don’t just ignore this disaster, for better or worse, transwarp beaming is now a part of this new TREK universe. Kind of. Just as before, it is ignored when it is convenient. As in, almost all of the time. For example, why can’t Starfleet just transwarp beam the bomb into the volcano? Why can’t they just beam the villain back from the planet he escapes to? Why do they need super-advanced stealth torpedoes, when they can now just beam a bomb directly onto a planet or near a starship? Why didn’t they just beam the Starfleet commanders out of the room being attacked? (You’d think “fire alarms” in the future would just beam everyone in the room to a safe place).

This is a problem that plagues every aspect of this new incarnation of Trek: “red matter” from the 2009 STAR TREK obviates the need for any other kind of weapon, magic blood means you can revive the dead, automated starships mean you now don’t need a crew, transwarp beaming means you don’t need starships at all! It is lazy writing for a moment of kewl-factor, ignoring the fundamental consequences down the road. The original Trek universe was one with a rules and a logical underpinning. That’s absolutely necessary for the audience to buy into such a fantastical concept. In this one, it seems almost anything goes, and things just happen willy-nilly because the writers wrote it that way.

WHO BUILT MY BATTLESHIP?

A major plot point in STAR TREK INTO OBSCURITY is that a new class of starship is secretly being built in Jupiter orbit. Stupidly, the characters refer to the location of this starship as a set of coordinates, as if the thing is static in space and not in orbit around a planet. Yes, I realize there are four coordinates, as if time is one of them. Still doesn’t work. Astronomers don’t use coordinates like this for a reason.

Ok, so they’re building a giant new starship that is bigger, faster, and tougher than the Enterprise, and is so automated it requires almost no crew AND CAN EVEN BE RUN BY A SINGLE PERSON. This is moronic. First of all, why risk the lives of hundreds of people at any point in the future by having a huge crew on a starship? And second, this means the Enterprise has to be rebuilt for the next movie, because there is no way Starfleet is sending them out there in light of the Klingon threat with obsolete tech.

Also, why does this badass starship have giant, cavernous hangars with hangar doors that are about ten feet in diameter? And why would the crew be “private security” if clearly tens of thousands of people in Starfleet know about this operation. First, it is a project of the admiral in charge of Starfleet. Second, he has a whole research division devoted to it. Third, it takes thousands of people to build a modern aircraft carrier -- a starship is surely no different. Clearly this is a project approved at the highest levels of Starfleet and whatever government exists on Earth in the 23rd century. They are going to be pissed about Kirk’s meddling.

COINCIDENCES

In my review of this movie’s predecessor, I mentioned how it was a crazy coincidence (i.e. lazy writing) that out of all the area on a planet, Kirk crash-lands right next to where Spock is hiding in a cave, and just happens to run into that cave. At least you could kind of explain that by saying that the Enterprise sent Kirk to near where the Starfleet base was, and that’s where hobo Spock was hanging out too. But in this movie, our heroes head to an abandoned part of Kronos, only to be intercepted by Klingon warbirds, leading them on a chase through this area of the planet. Just when our heroes think they are free, they are surrounding by Klingons and forced to surrender. And who should just happen to be hanging out exactly where they land? Our villain, John Harrison! And it wasn’t because they knew where he was -- they might have initially been headed to his last known coordinates, but then they got diverted by the chase. To keep this scientific, let’s say they are traveling at the speed of a 747: 250 km/s. If they are being chased for a 100 seconds, that means they traveled 25 km on the surface. Even if they knew John Harrison was somewhere along that line that they had traveled, and he could have run there from 100m away, there‘s still only a 1 in 250 chance that they wold have landed near him.

Also, if John Harrison has this device that can beam him anywhere in the galaxy, why did he go to the Klingon homeworld? Why did he bring massive guns and carry them around on the planet? An Earth man wandering a Klingon planet with a giant gun. That doesn’t attract attention. None of it makes any sense.

I could go on about a great many things: why did they need the villain’s blood when they had 72 superhumans on the ship, how can you just kick a nuclear reactor to get it restarted, why didn’t they beam Kirk to sickbay, etc. But I’m just tired of all the nonsense in this movie. This isn’t science fiction, it is just a Michael Bay-level mindless action film shoehorned into an overly convoluted, senseless plot.